Lattice-Model Sample Computations and Concept PDF

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Application of Lattice Model with sample situation...

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VALUATION OF BONDS WITH EMBEDDED OPTIONS LATTICE MODEL- used to value callable bonds. It employs binomial tree to show different paths the price of an underlying asset. Example: A callable bond with a 10% annual coupon will mature in two years. Assume that the bond can be called in one year at 100. The current one-year spot rate is 7.9%. For the second year, the yield-volatility model forecasts that the one-year rate will be either 6.8% or 7.6%. Using a lattice model, what is the current price?

100 10 102.2305 100 10 7.6%

104.3683 7.9%

100 10 102.9962 102.9962 10 6.8%

100 10

Year 0

Year 1

Year 2

The tree will have three nodal periods: 0, 1, and 2. The goal is to find the value at current year. We know the value for all the nodes in nodal period 2: V 2=100. In nodal period 1, there will be two possible prices: V1,U =[(100+10)/1.076+(100+10)/1.076]/2 = 102.2305 V1,L =[(100+10)/1.068+(100+10)/1.068]/2= 102.9962 Since V1,L is greater than the call price, the call price is entered into the formula below: V0=[(102.2305+10)/1.079)+(102.9962+10)/1.079)]/2 = 104.3683....